give answer in 2 step with explanation at the end of each step and final answer at the end: The following figure is the floor plan of an office complex. The room abbreviations are provided. ( include room V ) The outside hallway runs around the entire office complex but it is considered as one room. The doorways are shown on the floor plan by the triangle shape that connects certain rooms. 1 . In a graph modeling this situation, each vertex would represent a location ( type of room corresponding to the room abbreviation list ) and each edge would represent a door ( the endpoints of each edge would be the two rooms each door connects ) .  a . How many vertices would be in the graph? b . How many edges would be in the graph? 2 . Draw the graph that models this situation. draw the vertices. ( Each vertex needs to consist of a specific dot with the room abbreviation labeling it . ) After you have the vertices drawn and labeled, then you can insert the edges by connecting the vertices that represent the rooms that have doors connecting them on the floorplan. Make sure your amount of vertices and edges correspond to your answer to question 1 and to the actual amount of locations and doors shown on the floorplan. 3 . In the graph, are there any edges that act as bridges? Explain your answer. 4 . What are the degrees of each vertex on the graph? 5 . Is it possible to start and end in the outside hallway ( OH ) of the complex and walk through each door of the complex exactly once? Explain why or why not by using appropriate theorems and referring to your graph of the complex. 6 . Is it possible to start and end in different locations and walk through every door once in the complex? Explain why or why not by using appropriate theorems and referring to your graph of the complex. If it is possible, indicate what locations would be the starting and ending points. 7 . What edge would need to be duplicated on the graph in order to find an optimal eulerization of the graph? Explain your answer.The following figure is the floor plan of an office complex. The room abbreviations are provided. The outside hallway runs around the entire office complex but it is considered as one room. The doorways are shown on the floor plan by the triangle shape that connects certain rooms. oH Room Abbreviations: OH — Outside hallway 'W — Waiting room R — Reception area P — Presidents office lsT a] L — Large meeting room L H H - Hallway Si — Storage room 1 \ = S; — Storage room 2 Ci — Conference room 1 Cz — Conference room 2 SO — Secretary’s office CR — Computer room i} | A — Accountin;